Posted: November 13th, 2020

Capital Asset Pricing Model

Despite the appeal of the Capital Asset Pricing Model (CAPM), there have been many disputes on whether it is a good measure of the relationship between returns and risks. Since it was first developed by Sharp(1964), researchers have carried out a huge number of both theoretical and empirical tests on the original model as well as its newly developed versions. Although this has substantially improved the view on the CAPM, there are still non-trivial problems in the practical implementation of the model. This paper examines the validity of the CAPM on Australian data. Statistical tests will be carried out; alternative forms including international and externality-associated versions will be suggested and examined.
We focus on four questions. First, we investigate the explanatory power of betas for nine different Australian industries’ stock returns. Second, we ask whether the externality-associated model outperforms the original CAPM for Australian data. Third, we compare international model and the domestic one. Finally, we examine whether exchange rates play an important role in the success of an international CAPM. In other words, we are testing validity of Purchasing Power Parity in the international stock market.
Our paper is then structured as follows. In the next section, background theory and relevant literatures are briefly discussed. Specification, methodologies and variable definitions are then presented in section 3. Section 4 is the description of the data and analysis of their potential problems. In section 5, we carry out all the statistical tests for our preliminary hypotheses. Finally, section 6 includes conclusions and implications of our results; suggestions for further research are also put in this section.1

2. Back ground theory
The CAPM lays most of its groundwork on Markowitz mean-variance efficient problem (1959) which figures out an optimal (in terms of lowest risk) portfolio for investors in corresponding to their desired rate of returns. The original CAPM was officially developed by the works of Sharp(1964) and Lintner (1965b) with an introduction of risk free rate in the optimal portfolio. The major achievement from the CAPM was not how asset returns are determined from a portfolio of risk free asset and market portfolio but how risk is quantified under the model’s estimates (�). This success has attracted concerns of many researchers.
The model, hence, has been substantially tested and modified. One of the great works comes from Fama and French (1992, 1993, and 1996) where the authors criticised the ability of beta in explaining cross-sectional variation in equity returns. The other famous work comes from Black (1972) where he first introduces a non risk free asset model by replacing risk free assets by zero-beta assets. Moreover, different versions of the CAPM are also developed with the Arbitrage Pricing Theory (APT) model by Ross (1976) and Intertemporal Capital Asset Pricing Model (ICAPM) by Merton (1973a). The first version of international CAPM was discussed in Solnik(1974) then extended by Roll and Solnik(1975) and Grauer, et al(1976).
In related work, Brailsford, et al (1997) estimates betas on 14 Australian companies’ data during a ten-year period from January 1984 to December 1993. Using OLS, with ten-year bond futures yield and ASX All Ordinary Index as proxies for risk free rate and market rate respectively, they proved that betas are significant in explaining asset returns on market and risk free returns. For externality-associated model, Draper and Paudyal (1995), using dummy variables for seasonal effects, presents evidence that UK-stock betas are sensitive to days of week.
Moreover, Gultekin, et al (1989) finds that the performance of their model is affected by changes in capital control from the governments. In the international CAPM, while Cho, Eun, and Senbet (1986) rejects any improvement of the model from international effect, Korajczyk and Viallet(1989) contend that the rejection of international models is sensitive to inclusion of sample periods with strict capital control.
Our approach
Although there are many common points between our paper and others’, we can still easily see some important differences and improvements in our approach. First, in comparison with Brailsford et al (1997), although we are also using Australian data, we cover more stocks than they did yet with less sacrifice of estimation precision due to the dramatic increase in number of parameters. The technique which is used is to group assets into portfolios. By this, we not only reduce the number of parameters but also are able to classify assets into different industries.
Comparing to the international model of Korajczyk and Viallet (1989), our model is more flexible. In constructing an international market portfolio, instead of pooling all the data (both international and domestic) by their weights to form a new market portfolio like what Korajczyk and Viallet did we separate all our international indices to be different regressors in our model.
In our point of view, our approach is more realistic and flexible because we do not know proportions of the international assets in desired market portfolios of different investors. Different investors can choose their international market portfolios in very different ways, so letting the proportions of the foreign indices be naturally calculated from the data is an appropriate thing to do. Moreover, another advantage of separating market indices is that we can evaluate influences of different markets on Australia’s stock returns.
Finally, the inclusion of exchange rates in the international model is also our improvement from almost other international models. The value of international market indices are converted in Australian Dollar before calculating their returns and excess returns. In theory, this does not change the calculated returns if we convert the values or not as long as the purchasing power parity holds. However, in reality, we can never assure that this relationship holds, therefore, this approach can help us evaluate the effects of purchasing power parity on Australian stocks’ returns.